# Solve. 0.4y + 3 > 3.6y - 5

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**Apply Inequality Theorem # 1:** The direction of an inequality doesn't change if the same real number is added or subtracted to both sides

Add -3.6y to both sides, the direction doesn't change:

`0.4y-3.6+3> -5`

Add -3 to both sides, the direction doesn't change:

`0.4y-3.6y> -5-3`

Simplify each side:

`-3.2y> -8`

**Apply Inequality Theorem # 2:** The direction of an inequality doesn't change if both sides are multiplied or divided by the same real number.

Divide each side by 3.2, the direction doesn't change::

`-y> -8/3.2`

**Apply Inequality Theorem # 3:** The direction of an inequality is inverted when both sides are multiplied or divided by the same negative number.

Multiply both sides by -1, the direction changes:

`y<8/3.2`

Simplify:

`y<2.5`

**Therefore this inequality is true for all values of y<2.5**

0.4y + 3 > 3.6y - 5

move like terms to the same side by subtracting 3.6y and 3

you should end up with:

.4y - 3.6y > -3 - 5

combine like terms:

-3.2y > -8

since we are solving for y we divide by -3.2

-3.2y/-3.2 > -8/-3.2

simplify:

y < 2.5

the sign changes because you are dividing.

0.4y + 3 > 3.6y - 5

To solve this , first subtract 3.6y on both sides .

By subtracting both sides by 3.6y , you should get

-3.2y + 3 > -5 now subtract 3 on both sides

By subtracting 3 on both sides , you should get

-3.2y > -5 now divide both sides by -3.2

By dividing both sides by -3.2 , you should get

y < 2.5 which is your answer